Grant is reportedly ready to sell star duo Frank Lampard and Didier Drogba due to their allegiance to former Blues boss Jose Mourinho - and is believed to have told Roman Abramovich he wants to sign Kaka.
The Brazil international would reportedly cost a world-record £100million, with Abramovich apparently the only club owner who could afford the fee, according to the Daily Express.
If the Stamford Bridge club wished to sign the world player of the year nominee they would have to meet his astronomical buy-out clause at the Serie A side.
"Kaka is certainly a long-term target, and if there is any chance of getting him then Avram will try to make it happen. Avram likes Kaka very much and has told Abramovich he is a good investment, even at £100m," a source told the Daily Express.
"Of course all the wealthiest clubs in the world want Kaka, including Manchester United and Real Madrid, but only Chelsea could really afford him. Milan are not sellers but you never know if Chelsea made a big enough offer."
Grant wants to move forward from the Mourinho regime and make Chelsea more adventurous and sees Kaka as a far better option than the ageing, disco-loving Ronaldinho, who has also been linked with the club.